Consider the equation ∫(logex)^{1/2} / x(a-(logex)^{3/2})^2; x ∈ (1, e).

Question

Consider the equation \(\int\limits_1^e\) \(\frac{(log_ ex)^\frac{1}{2}}{x(a-(log_ e x)^{\frac{3}{2}})^2}\)

Which of the following statements is/are TRUE? 

(A) No α satisfies the above equation 

(B) An integer α satisfies the above equation 

(C) An irrational number α satisfies the above equation 

(D) More than one a satisfy the above equation

Answer 1

(C) An irrational number α satisfies the above equation  

(D) More than one a satisfy the above equation